Compactification of M Theory and Manifolds with G2 Holonomy

M 理论和流形的 G2 Holonomy 紧化

基本信息

批准号：
15540253
负责人：
EGUCHI Tohru
金额：
$ 2.18万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2006
项目状态：
已结题

项目摘要

In paper 2 we have applied the method of geometrical transition and computed the partition function of topological string theory on various non-compact Calabi-Yau manifolds using the link invariants of Chern-Simons theory. We have shown that the results of computation agree exactly with the formula proposed by Nekrasov for the N=2 supersymmetric gauge theory. And thus they establish the relation between topological string and N=2 SUSY gauge theory.In paper 3 we have used the representation theory of N=2 supersonformal algebra and the method of modular bootstrap and derived the boundary states of N=2 Liouville theory. N=2 Liouville theory is known to be T-dual to the coset SL(2;R)/U(1) model and our results on boundary states agree well with those known in SL(2;R)/U(1) theory.In paper 7 we have used the formula of Ashoke-Douglas for the distribution of flux vacua in type IIB string theory and evaluated the distribution function of flux vacua on the moduli space of Calabi-Yau manifolds. We have shown that the distribution function is peaked around the singular points in Calabi-Yau moduli space and have the universal behavior 1/(z^2 log z^2). Thus it diverges at the singular point z=0, however, it is still integrable around z=0 and there exist only a finite number of vacua around each Calabi-Yau singularity..In paper 8 we have studied the geometry of non-compact Calabi-Yau manifolds like ALE spaces and have proposed formula for their. elliptic genera based on the analysis of the representation theory of N=2,4 superconformal algebras. Our formula agrees with the one suggested from the decompactification of K3 surface by means of some non-trivial theta function identity.

在论文2中，我们采用了几何跃迁的方法，并使用Chern-Simons理论的链接不变式计算了拓扑字符串理论的分区函数。我们已经表明，计算的结果与Nekrasov对N = 2超对称仪理论提出的公式完全一致。因此，他们建立了拓扑字符串与n = 2 Susy仪理论之间的关系。在论文3中，我们使用了n = 2的代表理论，以及模块化自举的代数和模块化自举的方法，并得出了n = 2 liouville理论的边界状态。 N=2 Liouville theory is known to be T-dual to the coset SL(2;R)/U(1) model and our results on boundary states agree well with those known in SL(2;R)/U(1) theory.In paper 7 we have used the formula of Ashoke-Douglas for the distribution of flux vacua in type IIB string theory and evaluated the distribution function of flux vacua on the moduli space of Calabi-Yau manifolds.我们已经表明，分布函数在Calabi-yau模量空间中的单数点周围达到峰值，并具有通用行为1/（z^2 log z^2）。因此，它在奇数点z = 0处有分歧，但是，它仍然可以在z = 0左右进行集成，并且在每个calabi-yau奇异性周围仅存在有限数量的真空。.在论文8中，我们研究了非紧凑型calabi-yau歧管的几何形状，例如ALE空间，并提供了建议的公式。基于n = 2,4超符号代数的表示理论的分析的椭圆属。我们的公式与通过某些非平凡的theta函数身份对K3表面的分解所建议的公式一致。